As shown in Lewis et al. (2017), fuel swelling in nuclear fuel is caused by the presence of fission gases in small bubbles. Consider a gas bubble of radius \(R\) embedded in a solid medium with no hydrostatic stress, where the pressure \(p\) acting to expand the bubble is balanced by the surface tension \(\gamma\) of the solid (see Fig. 11.3). Using Buckingham's \(\pi\) theorem, determine the dependence of the pressure on the bubble radius and solid surface tension. For this analysis, use the basic physical dimensions for the system of force (F), length (L), and time (T).

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FIGURE 11.3 R Solid Gas pressure, p Surface tension, y